Multiply the following complex numbers, marked as blue dots on the graph: $(2 e^{7\pi i / 12}) \cdot (4 e^{2\pi i / 3})$ (Your current answer will be plotted in orange.)
Answer: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $2 e^{7\pi i / 12}$ ) has angle $\frac{7}{12}\pi$ and radius $2$ The second number ( $4 e^{2\pi i / 3}$ ) has angle $\frac{2}{3}\pi$ and radius $4$ The radius of the result will be $2 \cdot 4$ , which is $8$ The angle of the result is $\frac{7}{12}\pi + \frac{2}{3}\pi = \frac{5}{4}\pi$ The radius of the result is $8$ and the angle of the result is $\frac{5}{4}\pi$.